Extremal chiral ring states in AdS/CFT are described by free fermions for a generalized oscillator algebra

Understand

This paper studies a special class of states for the dual conformal field theories associated with supersymmetric $AdS_5\times X$ compactifications, where $X$ is a Sasaki-Einstein manifold with additional $U(1)$ symmetries.

• Under appropriate circumstances, it is found that elements of the chiral ring that maximize the additional $U(1)$ charge at fixed R-charge are in one to one correspondence with multitraces of a single composite field.
• This is also equivalent to Schur functions of the composite field.
• It is argued that in the formal zero coupling limit that these dual field theories have, the different Schur functions are orthogonal.